Solve 32/5+22/35div111/25-3/7

$$3 \frac { 2 } { 5 } + 2 \frac { 2 } { 35 } \div 1 \frac { 11 } { 25 } - \frac { 3 } { 7 }$$

Evaluate

$$\frac{22}{5}=4.4$$

Solution Steps

Multiply 3 and 5 to get 15.

$$\frac{15+2}{5}+\frac{\frac{2\times 35+2}{35}}{\frac{1\times 25+11}{25}}-\frac{3}{7}$$

Add 15 and 2 to get 17.

$$\frac{17}{5}+\frac{\frac{2\times 35+2}{35}}{\frac{1\times 25+11}{25}}-\frac{3}{7}$$

Divide \frac{2\times 35+2}{35} by \frac{1\times 25+11}{25} by multiplying \frac{2\times 35+2}{35} by the reciprocal of \frac{1\times 25+11}{25}.

$$\frac{17}{5}+\frac{\left(2\times 35+2\right)\times 25}{35\left(1\times 25+11\right)}-\frac{3}{7}$$

Cancel out 5 in both numerator and denominator.

$$\frac{17}{5}+\frac{5\left(2+2\times 35\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 2 and 35 to get 70.

$$\frac{17}{5}+\frac{5\left(2+70\right)}{7\left(11+25\right)}-\frac{3}{7}$$

Add 2 and 70 to get 72.

$$\frac{17}{5}+\frac{5\times 72}{7\left(11+25\right)}-\frac{3}{7}$$

Multiply 5 and 72 to get 360.

$$\frac{17}{5}+\frac{360}{7\left(11+25\right)}-\frac{3}{7}$$

Add 11 and 25 to get 36.

$$\frac{17}{5}+\frac{360}{7\times 36}-\frac{3}{7}$$

Multiply 7 and 36 to get 252.

$$\frac{17}{5}+\frac{360}{252}-\frac{3}{7}$$

Reduce the fraction \frac{360}{252} to lowest terms by extracting and canceling out 36.

$$\frac{17}{5}+\frac{10}{7}-\frac{3}{7}$$

Least common multiple of 5 and 7 is 35. Convert \frac{17}{5} and \frac{10}{7} to fractions with denominator 35.

$$\frac{119}{35}+\frac{50}{35}-\frac{3}{7}$$

Since \frac{119}{35} and \frac{50}{35} have the same denominator, add them by adding their numerators.

$$\frac{119+50}{35}-\frac{3}{7}$$

Add 119 and 50 to get 169.

$$\frac{169}{35}-\frac{3}{7}$$

Least common multiple of 35 and 7 is 35. Convert \frac{169}{35} and \frac{3}{7} to fractions with denominator 35.

$$\frac{169}{35}-\frac{15}{35}$$

Since \frac{169}{35} and \frac{15}{35} have the same denominator, subtract them by subtracting their numerators.

$$\frac{169-15}{35}$$

Subtract 15 from 169 to get 154.

$$\frac{154}{35}$$

Reduce the fraction \frac{154}{35} to lowest terms by extracting and canceling out 7.

$$\frac{22}{5}$$

Factor

$$\frac{2 \cdot 11}{5} = 4\frac{2}{5} = 4.4$$